Mixture between populations is a fundamental process that shapes biology, genetic variation, and the risk for disease. Despite its importance, the analytical methods that are available to study mixture on a genome-wide scale are limited. This makes it a priority to develop methods that can analyze this history in the large data sets that are now practical to generate. No federal grant currently supports the development of such methods. This grant proposes to develop methods and make software available for studying mixture. The Aims are: (1) To develop tools that make inferences about mixture based on allele frequency and haplotype frequency differences. (2) To develop tools that estimate dates of mixture based on admixture linkage disequilibrium and genetic divergence data. We expect that this grant will be of value in three areas. (a) It will support the development of methods and user-friendly software that will be important for evolutionary and medical genetics. (b) It will support work that will result in insights relevant to finding disease genes in human populations that are recently or anciently admixed. (c) It will lead to new insights about human history as well as the history of other organisms. The connection to medical genetics is particularly important. Our laboratory's past work on the evolutionary history of populations has been intertwined with our work on disease gene mapping, and the approaches that we developed in both areas were synergistic. In particular, we have leveraged the history of admixture in human populations to make new gene discoveries and to understand variation in disease risk across populations. We expect to be able to make further connections between evolutionary and medical genetics by developing sophisticated approaches for understanding and modeling population mixture.